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Formal logic provides us with a powerful set of techniques for criticizing some arguments and showing others to be valid. These techniques are relevant to all of us with an interest in being skilful and accurate reasoners. In this highly accessible book, Peter Smith presents a guide to the fundamental aims and basic elements of formal logic. He introduces the reader to the languages of propositional and predicate logic, and then develops formal systems for evaluating arguments translated into these languages, concentrating on the easily comprehensible 'tree' method. His discussion is richly illustrated with worked examples and exercises. A distinctive feature is that, alongside the formal work, there is illuminating philosophical commentary. This book will make an ideal text for a first logic course, and will provide a firm basis for further work in formal and philosophical logic.
With the same intellectual goals as the first edition, this innovative introductory logic textbook explores the relationship between natural language and logic, motivating the student to acquire skills and techniques of formal logic. This new and revised edition includes substantial additions which make the text even more useful to students and instructors alike. Central to these changes is an Appendix, 'How to Learn Logic', which takes the student through fourteen compact and sharply directed lessons with exercises and answers.
Aimed at undergraduates and graduates in computer science, logic, mathematics, and philosophy, this text is a lively and entertaining introduction to formal logic and provides an excellent insight into how a simple logic works.
Provides an introduction to formal, deductive logic using Socratic dialogue and discussion.
Intended for a course for beginning students in philosophy, mathematics, linguistics, or computer science. Motivation for each formal concept and each step in building a formal logic in terms of formalizing reasoning. Provides a conception of formal logic and not just a collection of results. Summaries at important junctures in the book keep students aware of what they're doing and where they're going. Hundreds of exercises that teach. Criteria of formalization with many examples of formalizing ordinary language reasoning in an example-analysis format. A complete course: syntax, semantics, and completeness theorems for classical propositional logic and classical predicate logic, and syntax and semantics for second-order classical predicate logic."
In 1931, the young Kurt Gödel published his First Incompleteness Theorem, which tells us that, for any sufficiently rich theory of arithmetic, there are some arithmetical truths the theory cannot prove. This remarkable result is among the most intriguing (and most misunderstood) in logic. Gödel also outlined an equally significant Second Incompleteness Theorem. How are these Theorems established, and why do they matter? Peter Smith answers these questions by presenting an unusual variety of proofs for the First Theorem, showing how to prove the Second Theorem, and exploring a family of related results (including some not easily available elsewhere). The formal explanations are interwoven with discussions of the wider significance of the two Theorems. This book - extensively rewritten for its second edition - will be accessible to philosophy students with a limited formal background. It is equally suitable for mathematics students taking a first course in mathematical logic.

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